An inverse problems perspective on machine learning and optimization
Prof. Lorenzo Rosasco, Università di Genova e Massachusetts Institute of Technology.
Sala conferenze IMATI-CNR, Pavia - Tuesday, March 20, 2018 h.15:00
Abstract. A stunning variety and quantity of data is constantly generated by novel technologies, experimental sciences as well social sciences. This data deluge, and corresponding huge potential source of information, is the basis of what has been called a data revolution. At the root of this revolution is machine learning: a branch of artificial intelligence studying and developing systems that are trained on data, rather than being solely programmed. From a mathematical point of view, machine learning is at its core a statistical inference problem: past data are used to train algorithms to ``learn'' how to deal with future data. However, compared to classical statistics, algorithmic and computational aspects have a predominant role in machine learning. Indeed, much of current research is devoted to either one of these two aspects.
In this talk we argue for the need to transcend this dichotomy between statistical and computational aspects and suggest how inverse problems and regularization theory can provide a natural framework towards this end. The talk will be divided in two parts. In the first, we will show how machine learning can be formulated as a linear inverse problem with a specific stochastic data model. In the second, we will develop this connection to derive novel algorithmic solutions to learn from massive data sets. Theoretical and experimental results show how the proposed approaches allow for optimal statistical accuracy as well minimal computational complexity.
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